<p>Using the KP hierarchy reduction method, we investigate the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal{P}\mathcal{T}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">P</mi> <mi mathvariant="script">T</mi> </mrow> </math></EquationSource> </InlineEquation>-symmetric nonlocal Maccari system, which serves as a two-dimensional extension of the nonlocal nonlinear Schrödinger equation. A family of exact lump–soliton solutions on a trigonometric periodic line-wave background is constructed in the form of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(2J+1)\times (2J+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>J</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> Gram-type determinants. Under different parameter restrictions, both normal and anomalous interaction between localized lump waves and line solitons are revealed. Localized energy can propagate elastically through line solitons, exhibiting wave-like behavior, or be annihilated or radiated by line solitons through fusion and fission mechanisms. These results indicate that nonlocal systems not only admit solutions satisfying <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal{P}\mathcal{T}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">P</mi> <mi mathvariant="script">T</mi> </mrow> </math></EquationSource> </InlineEquation> symmetry, but also support various types of interaction processes commonly observed in local systems. Compared with previously reported breather, rogue-wave and lump solutions on nonzero or periodic backgrounds, the present solutions emphasize mixed lump–line-soliton interactions and their asymptotic mechanisms on a trigonometric periodic line-wave background.</p>

Dynamical asymptotic analysis for the $\mathcal{P}\mathcal{T}$-symmetric nonlocal Maccari system: the superposition of lump and solitons on a periodic line wave background

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2026年8月5日

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Yulei Cao,
Li Jing,
Zhao Zhang

摘要

Using the KP hierarchy reduction method, we investigate the $\mathcal{P}\mathcal{T}$ $P T$ -symmetric nonlocal Maccari system, which serves as a two-dimensional extension of the nonlocal nonlinear Schrödinger equation. A family of exact lump–soliton solutions on a trigonometric periodic line-wave background is constructed in the form of $(2J+1)\times (2J+1)$ $(2 J + 1) \times (2 J + 1)$ Gram-type determinants. Under different parameter restrictions, both normal and anomalous interaction between localized lump waves and line solitons are revealed. Localized energy can propagate elastically through line solitons, exhibiting wave-like behavior, or be annihilated or radiated by line solitons through fusion and fission mechanisms. These results indicate that nonlocal systems not only admit solutions satisfying $\mathcal{P}\mathcal{T}$ $P T$ symmetry, but also support various types of interaction processes commonly observed in local systems. Compared with previously reported breather, rogue-wave and lump solutions on nonzero or periodic backgrounds, the present solutions emphasize mixed lump–line-soliton interactions and their asymptotic mechanisms on a trigonometric periodic line-wave background.

Dynamical asymptotic analysis for the \(\mathcal{P}\mathcal{T}\)-symmetric nonlocal Maccari system: the superposition of lump and solitons on a periodic line wave background

摘要